A158641 Strong primes p: adding 2 to any one digit of p produces a prime number (no digits 8 & 9 in p).

3, 5, 11, 17, 41, 107, 137, 347, 2111, 2657, 3527, 4421, 6761, 21011, 24371, 32057

Offset: 1

Author

Zak Seidov, Mar 23 2009

Keywords

• nonn
• full
• fini
• base

Comments

All terms are lesser of twin pairs.

The sequence is finite. In particular, there are no terms longer than 5 digits since 2*10^k for k=0,1,...,5 give all nonzero residues modulo 7, implying that adding 2 to some digit yields a multiple of 7. - Max Alekseyev, Apr 25 2010

Examples

			2111 is in this sequence because all 2111, 4111, 2311, 2131 and 2113 are prime numbers.
32057 is in this sequence because all 32057, 52057, 34057, 32257, 32077 and 32059 are prime numbers.
		

Crossrefs

Cf. A050249, A158124, A158125 Weakly prime numbers (changing any one digit always produces a composite number).

Programs

Maple

Lton := proc(L) local i; add(op(i,L)*10^(i-1),i=1..nops(L)) ; end: isA158641 := proc(p) local pdgs,pplus,i ; if isprime(p) then pdgs := convert(p,base,10) ; if convert(pdgs,set) intersect {8,9} <> {} then false; else for i from 1 to nops(pdgs) do pplus := subsop(i=2+op(i,pdgs),pdgs) ; if not isprime(Lton(pplus)) then RETURN(false); fi; od: true; fi; else false; fi; end: for n from 1 do p := ithprime(n) ; if isA158641(p) then print(p) ; fi; od: # R. J. Mathar, Apr 16 2009

Mathematica

spQ[p_]:=Max[IntegerDigits[p]]<8&&AllTrue[FromDigits/@Table[MapAt[ 2+#&,IntegerDigits[ p],n],{n,IntegerLength[p]}],PrimeQ]; Select[Prime[ Range[ 3500]],spQ] (* Harvey P. Dale, Nov 26 2022 *)

PARI

test(p)=my(v=eval(Vec(Str(p)))); for(i=1,#v, if(v[i]>7,return(0))); for(i=0,#v-1, if(!isprime(p+2*10^i), return(0))); 1
forprime(p=2,4e9, if(isprime(p+2) && test(p), print1(p","))) \\ Charles R Greathouse IV, Sep 09 2009

PARI

has(n)=if(vecmax(Set(digits(n)))>7, return(0)); for(i=0,#digits(n)-1, if(!isprime(n+2*10^i), return(0))); 1
select(has, primes(3438)) \\ Charles R Greathouse IV, Mar 11 2016

Extensions

Keywords full, fini from Max Alekseyev, Apr 25 2010